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Since each photon only has an energy equivalent to the mass of one electron it can't undergo pair production- there's nothing with a mass of half an electron that it could form a pair of.

A photon can have any energy you want, photons in the visible range have energy around 1 eV, an electron's mass is 511*10³ eV/c²...

In general photons can have any energy you want.
In the case of photons produced by pair production from electron + positron annihilation they have an energy of 511KeV. Unless the particles had a lot of energy to begin with, the photon energies produced will not be big enough to produce a particle by pair production beccause there isn't a particle with a mass of about 255 KeV.

Ok, I thought you answered to the OP's question about why two photons and not one only are generated in the e⁺ e^- annihilation.

BTW, does anyone know why SLAC would be colliding massless changeless particles like photons?

Photon-photon collisions are studied since the 70', i imagine it's just for research, as every other kind of research, why your question?